Calculation of tunnel splitting in a biaxial spin particle with an applied magnetic field

The level splitting formulae of excited states as well as ground state for a biaxial spin particle in the presence of an applied magnetic field are obtained in a simple way from Schrödinger theory. Considering the boundary condition of the wave function, we obtain the tunneling splitting of the energy levels for half-integral spins as well as for the integral spins. The results obtained are compared with those previously derived by complicated pseudoparticle methods and numerical calculation values.postprin

Dynamics of one-dimensional tight-binding models with arbitrary time-dependent external homogeneous fields

The exact propagators of two one-dimensional systems with time-dependent external fields are presented by following the path-integral method. It is shown that the Bloch acceleration theorem can be generalized to the impulse-momentum theorem in quantum version. We demonstrate that an evolved Gaussian wave packet always keeps its shape in an arbitrary time-dependent homogeneous driven field. Moreover, that stopping and accelerating of a wave packet can be achieved by the pulsed field in a diabatic way.Comment: 8 pages, 6 figure

Constructing L2-SVM-based fuzzy classifiers in high-dimensional space with automatic model selection and fuzzy rule ranking

In this paper, a new scheme for constructing parsimonious fuzzy classifiers is proposed based on the L2-support vector machine (L2-SVM) technique with model selection and feature ranking performed simultaneously in an integrated manner, in which fuzzy rules are optimally generated from data by L2-SVM learning. In order to identify the most influential fuzzy rules induced from the SVM learning, two novel indexes for fuzzy rule ranking are proposed and named as α-values and ω-values of fuzzy rules in this paper. The α-values are defined as the Lagrangian multipliers of the L2-SVM and adopted to evaluate the output contribution of fuzzy rules, while the ω-values are developed by considering both the rule base structure and the output contribution of fuzzy rules. As a prototype-based classifier, the L2-SVM-based fuzzy classifier evades the curse of dimensionality in high-dimensional space in the sense that the number of support vectors, which equals the number of induced fuzzy rules, is not related to the dimensionality. Experimental results on high-dimensional benchmark problems have shown that by using the proposed scheme the most influential fuzzy rules can be effectively induced and selected, and at the same time feature ranking results can also be obtained to construct parsimonious fuzzy classifiers with better generalization performance than the well-known algorithms in literature. © 2007 IEEE

Low-level interpretability and high-level interpretability: a unified view of data-driven interpretable fuzzy system modelling

This paper aims at providing an in-depth overview of designing interpretable fuzzy inference models from data within a unified framework. The objective of complex system modelling is to develop reliable and understandable models for human being to get insights into complex real-world systems whose first-principle models are unknown. Because system behaviour can be described naturally as a series of linguistic rules, data-driven fuzzy modelling becomes an attractive and widely used paradigm for this purpose. However, fuzzy models constructed from data by adaptive learning algorithms usually suffer from the loss of model interpretability. Model accuracy and interpretability are two conflicting objectives, so interpretation preservation during adaptation in data-driven fuzzy system modelling is a challenging task, which has received much attention in fuzzy system modelling community. In order to clearly discriminate the different roles of fuzzy sets, input variables, and other components in achieving an interpretable fuzzy model, a taxonomy of fuzzy model interpretability is first proposed in terms of low-level interpretability and high-level interpretability in this paper. The low-level interpretability of fuzzy models refers to fuzzy model interpretability achieved by optimizing the membership functions in terms of semantic criteria on fuzzy set level, while the high-level interpretability refers to fuzzy model interpretability obtained by dealing with the coverage, completeness, and consistency of the rules in terms of the criteria on fuzzy rule level. Some criteria for low-level interpretability and high-level interpretability are identified, respectively. Different data-driven fuzzy modelling techniques in the literature focusing on the interpretability issues are reviewed and discussed from the perspective of low-level interpretability and high-level interpretability. Furthermore, some open problems about interpretable fuzzy models are identified and some potential new research directions on fuzzy model interpretability are also suggested. Crown Copyright © 2008

Extracting takagi-sugeno fuzzy rules with interpretable submodels via regularization of linguistic modifiers

In this paper, a method for constructing Takagi-Sugeno (TS) fuzzy system from data is proposed with the objective of preserving TS submodel comprehensibility, in which linguistic modifiers are suggested to characterize the fuzzy sets. A good property held by the proposed linguistic modifiers is that they can broaden the cores of fuzzy sets while contracting the overlaps of adjoining membership functions (MFs) during identification of fuzzy systems from data. As a result, the TS submodels identified tend to dominate the system behaviors by automatically matching the global model (GM) in corresponding subareas, which leads to good TS model interpretability while producing distinguishable input space partitioning. However, the GM accuracy and model interpretability are two conflicting modeling objectives, improving interpretability of fuzzy models generally degrades the GM performance of fuzzy models, and vice versa. Hence, one challenging problem is how to construct a TS fuzzy model with not only good global performance but also good submodel interpretability. In order to achieve a good tradeoff between GM performance and submodel interpretability, a regularization learning algorithm is presented in which the GM objective function is combined with a local model objective function defined in terms of an extended index of fuzziness of identified MFs. Moreover, a parsimonious rule base is obtained by adopting a QR decomposition method to select the important fuzzy rules and reduce the redundant ones. Experimental studies have shown that the TS models identified by the suggested method possess good submodel interpretability and satisfactory GM performance with parsimonious rule bases. © 2006 IEEE

Constructing accurate and parsimonious fuzzy models with distinguishable fuzzy sets based on an entropy measure

Parsimony is very important in system modeling as it is closely related to model interpretability. In this paper, a scheme for constructing accurate and parsimonious fuzzy models by generating distinguishable fuzzy sets is proposed, in which the distinguishability of input space partitioning is measured by a so-called "local" entropy. By maximizing this entropy measure the optimal number of merged fuzzy sets with good distinguishability can be obtained, which leads to a parsimonious input space partitioning while preserving the information of the original fuzzy sets as much as possible. Different from the existing merging algorithms, the proposed scheme takes into account the information provided by input-output samples to optimize input space partitioning. Furthermore, this scheme possesses the ability to seek a balance between the global approximation ability and distinguishability of input space partitioning in constructing Takagi-Sugeno (TS) fuzzy models. Experimental results have shown that this scheme is able to produce accurate and parsimonious fuzzy models with distinguishable fuzzy sets. © 2005 Elsevier B.V. All rights reserved

Acupuncture in Treating Hepatic Fibrosis: A Review with Recommendation for Future Studies

Hepatic fibrosis, as a major medical problem, is characterized with significant morbidity and mortality. Acupuncture has potential advantages in treating hepatic fibrosis as acupuncture functions well to reduce Qi and Blood stagnation, resolve stasis and enhance body immunity, which are important factors in treating hepatic fibrosis. The aim of this review was to appraise the current limited evidence of acupuncture in treating hepatic fibrosis from both animal experiments and clinical trials by using both Chinese and western databases and to provide recommendations for future studies

AN UNSUPERVISED KERNEL BASED FUZZY C-MEANS CLUSTERING ALGORITHM WITH KERNEL NORMALISATION

In this paper, a novel procedure for normalising Mercer kernel is suggested firstly. Then, the normalised Mercer kernel techniques are applied to the fuzzy c-means (FCM) algorithm, which leads to a normalised kernel based FCM (NKFCM) clustering algorithm. In the NKFCM algorithm, implicit assumptions about the shapes of clusters in the FCM algorithm is removed so that the new algorithm possesses strong adaptability to cluster structures within data samples. Moreover, a new method for calculating the prototypes of clusters in input space is also proposed, which is essential for data clustering applications. Experimental results on several benchmark datasets have demonstrated the promising performance of the NKFCM algorithm in different scenarios. </jats:p

Classifying mental tasks based on features of higher-order statistics from EEG signals in brain-computer interface

In order to characterize the non-Gaussian information contained within the EEG signals, a new feature extraction method based on bispectrum is proposed and applied to the classification of right and left motor imagery for developing EEG-based brain-computer interface systems. The experimental results on the Graz BCI data set have shown that based on the proposed features, a LDA classifier, SVM classifier and NN classifier outperform the winner of the BCI 2003 competition on the same data set in terms of either the mutual information, the competition criterion, or misclassification rate. © 2007 Elsevier Inc. All rights reserved

The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation

A minimum dominating set for a digraph (directed graph) is a smallest set of vertices such that each vertex either belongs to this set or has at least one parent vertex in this set. We solve this hard combinatorial optimization problem approximately by a local algorithm of generalized leaf removal and by a message-passing algorithm of belief propagation. These algorithms can construct near-optimal dominating sets or even exact minimum dominating sets for random digraphs and also for real-world digraph instances. We further develop a core percolation theory and a replica-symmetric spin glass theory for this problem. Our algorithmic and theoretical results may facilitate applications of dominating sets to various network problems involving directed interactions.Comment: 11 pages, 3 figures in EPS forma